arXiv:2505. 15284v2 Announce Type: replace Abstract: Out-of-Distribution (OoD) detection is vital for the reliability of deep neural networks, the key of which lies in effectively characterizing the disparities between OoD and In-Distribution (InD) data.
arXiv:2606. 04930v1 Announce Type: cross Abstract: Real-time data analysis requires the ability to accurately and adaptively address nonlinear dynamics in a nonstationary data stream while preserving computational efficiency.
arXiv:2606. 26973v1 Announce Type: cross Abstract: Open-set semi-supervised learning aims to leverage unlabeled data that may contain out-of-distribution outliers while maintaining performance on in-distribution classes.
The paper studies Online Kernel Supervised Principal Component Analysis (OKSPCA), which uses random features and an Adam-style orthonormal basis update to optimize a supervised spectral objective. It shows that accurate optimization of this objective does not guarantee accurate population subspace recovery or improved predictive performance, and it provides theoretical results on consistency, concentration, and perturbation of the estimator. Empirical experiments on six benchmarks reveal that replacing the tracker with the exact empirical target does not significantly change regression deficits, while classification-rank models capture most of the terminal objective energy but can exhibit substantial geometric deviation; sample-size studies further separate empirical accuracy from population recovery. The diagnostics also compare computational trade-offs, indicating that exact on-request computation can be faster in classification settings, whereas Adam saves time relative to full thin‑SVD in some dense regression requests, despite persistent geometric error.
The paper tackles two key gaps in streaming PCA using Oja's algorithm: it establishes sharp operator‑norm convergence for general‑rank subspaces under sub‑Gaussian data, and it provides distributional inference for the resulting subspace estimator. The authors remove non‑vanishing remainder terms from existing analyses, achieving rates that match minimax bounds in both dense‑tail and sparse‑tail regimes. They further develop a linearization of Oja’s iterates, enabling high‑dimensional Gaussian approximations and an online multiplier bootstrap for practical inference.
arXiv:2607. 05201v1 Announce Type: new Abstract: In non-stationary streaming environments, simultaneously adapting to complex, non-linear domain shifts via continual learning while mitigating the catastrophic effects of severe, uncalibrated label noise poses a fundamental mathematical challenge.
arXiv:2510. 24043v4 Announce Type: replace Abstract: This paper presents Two-Stage LKPLO, a novel multi-stage outlier detection framework that overcomes the coexisting limitations of conventional projection-based methods: their reliance on a fixed statistical metric and their assumption of a single data structure.
arXiv:2605.15240v2 Announce Type: replace-cross Abstract: This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalizatio...
The paper investigates diffusion models trained in a lazy high‑dimensional regime, extending benign overfitting theory to generative settings. By analyzing denoising score matching in a vector‑valued RKHS with an inner‑product kernel, the authors derive exact risk trajectories under gradient flow when the number of samples scales proportionally with dimensionality. These trajectories reveal three distinct phases—spectral generalization, noise‑dominated interpolation, and empirical Bayes memorization—whose interplay shapes the distribution of generated samples.
arXiv:2608. 04227v1 Announce Type: new Abstract: We propose a family of random feature maps for scalable kernel machines on low-dimensional subspaces, ie on the Grassmannian manifold.
arXiv:2606. 06233v1 Announce Type: cross Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques.
arXiv:2503. 05169v2 Announce Type: replace Abstract: Applying machine learning to increasingly high-dimensional problems with sparse or biased training data increases the risk that a model is used on inputs outside its training domain.